Design method for compact waveguide mode control and converter devices

ABSTRACT

A method for designing an aperiodic grating structure for mode conversion and control which is based upon an inverse scattering optimization procedure. In accordance with this method, no predetermined shape or material variation of the grating structure is assumed. A constrained domain of all surfaces and material variations is searched to find an optimum aperiodic conversion surface profile for maximum conversion efficiency into the required output mode(s) or optimum control. Accordingly, the present method results in the design of rough surfaces or non-homogeneous structures for mode conversion and control. Because this method relies on scattering produced by short, forceful field perturbations, it is possible to achieve very small conversion lengths which are much less than one grating period. For microwave frequencies this method can be used to design mode converters, mode filters, frequency filters, phase shifters, mode launchers, waveguide transitions and adapters, power splitters, phase shifters, couplers, etc. Optical applications of this method include and are not limited to the design of waveguide transitions and couplers, mode converters, aperiodic gratings, aperiodic Bragg reflectors, narrowband filters, holographic elements, etc. In all these cases the propagation medium may be a waveguide of any shape, material and size, or it could be free space. Efficiencies close to the theoretical maximums are obtainable with this method.

REFERENCE TO RELATED PROVISIONAL PATENT APPLICATION

This application claims the benefit of United States Provisional PatentApplication Ser. No. 60/010,160 filed Jan. 18, 1996, the entirety ofwhich is hereby incorporated herein by reference as if set forth in fullherein.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention is directed to the field of microwave and opticalwaveguides. More particularly, the invention is directed to methods fordesigning compact mode control and converter elements for use withmicrowave and optical waveguides.

2. The Background Art

Mode control and conversion devices find wide application, for example,in microwave heating of plasmas for fusion experiments, multi-mode feedsfor RADAR systems, microwave waveguide transitions, couplers and modefilters, microwave waveguide mode launchers for waveguide transmissionsystems and for laboratory demonstrations, microwave heating systems andoptical waveguide couplers, mode converters and mode filters optical andmicrowave gratings, holographic elements, filters, phase shifters andthe like.

Mode converters have been extensively used to convert outputs of highpower microwave sources into lower order modes for plasma heating andlow loss microwave transmission.

Currently, periodic gratings are used for conversion of modes in highlyovermoded circular waveguides. These gratings are formed by periodicallyvarying the waveguide radius resulting in a rippled wall structure andare usually analyzed by coupled mode theory. Such rippled wallstructures result in very slight periodic field perturbations. Very highefficiencies have been reported for these gratings, but their lengthsremain large compared to the waveguide transverse dimension. Varioustechniques have been implemented to reduce the length of these gratings,but the overall conversion length remains limited by the grating period.Minimal scattering occurs in such designs and a minimum achievableconversion length appears to be equal to one grating period. See, e.g.,K. Kumric et al., "Optimization of Mode Converters for Generating theFundamental TE₀₁ Mode from TE₀₆ Gyrotron Output at 140 GHz,"International Journal of Electronics, Vol. 64 (January, 1988), pp.77-94, and M. J. Buckley et al., "Compact Quasi-Periodic and AperiodicTE_(ON) Mode Converters in Overmoded Circular Waveguides for use withGyrotrons," I.E.E.E. Transactions of Microwave Theory and Techniques,Vol. 38, No. 6 (June, 1990), pp. 712-721. Similar structures in the formof gratings have been designed for optical waveguides. See, e.g., D.Marcuse, "Mode Conversion Caused by Surface Imperfections of aDielectric Slab Waveguide," Bell Systems Technical Journal (December,1969) pp. 3187-3215. All of these converter designs are relativelylengthy when compared to the radial dimension of the waveguide. Atypical periodic grating mode converter is diagrammed in FIG. 1. In FIG.1 a first input electromagnetic wavefront 10 is applied to the converter12. The first wavefront 10 is formed of one or more modes. Afterinteraction with converter 12, which is much longer than it is wide, asecond electromagnetic wavefront 14 of the selected modality is outputfrom converter 12. Such converters are typically 95-99.5% efficient.

Mode filters for high power microwave sources whose output power isdistributed in various modes, permit extraction of a single mode at theoutput. Previous designs have not proven themselves particularlyefficient. See, e.g., J. P. Tate, et al., "ExperimentalProof-of-Principal Results on a Mode-Selective Input Coupler forGyrotron Applications", I.E.E.E. Transactions on Microwave Theory andTechniques", Vol. 42, No. 10 (October, 1994), pp. 1910-1917, and U.S.Pat. No. 3,771,078 dated Nov. 6, 1973 to H. G. Kidner, et al.

Mode launchers for efficiently exciting a specific mode into anovermoded waveguide can be difficult to construct. However, for a singlemode waveguide only one mode survives and thus the mode purity isensured.

Waveguide adapters, such as tapered sections, are generally used to joinwaveguides of unequal radial dimensions. Due to a gradual taper thesedevices are very long as compared to the radial waveguide dimension.See, e.g., W. A. Huting et al., "Numerical Solution of the ContinuousWaveguide Transition Problem," I.E.E.E. Transactions on Microwave Theoryand Techniques, Vol. 36, No. 11 (November, 1989), pp. 1802-1818.

Grating couplers can be used to couple free space light into an opticalwaveguide or vice versa and also for coupling between adjacentwaveguides. See, e.g., Nishihara, Haruna and Suhara, "Optical IntegratedCircuits", McGraw-Hill Optical and Electro-optical Engineering Series,1989.

Accordingly, a method for designing more compact, yet equally efficientmode converters and control elements for microwave and opticalapplications would be highly desirable.

SUMMARY OF THE INVENTION

The present invention is directed toward the design of an aperiodicgrating for mode conversion (defined as any operation on an input set ofmodes) which is based upon an inverse scattering optimization procedure.In accordance with this method, no predetermined shape of the gratingstructure is assumed. A constrained domain of all surfaces is searchedto find an optimum aperiodic conversion surface profile for maximumconversion efficiency into the required output mode(s). Accordingly, thepresent method results in the design of rough surfaces ornon-homogeneous structures for mode conversion. Because this methodrelies on scattering produced by short, forceful field perturbations, itis possible to achieve very small conversion lengths which are much lessthan one grating period. Precisely because periodic structures are notinitially assumed, compact or rough structures are generally obtained.This method can be used to design mode converters, mode filters,waveguide adapters, mode launchers, power splitters and combiners, phaseshifters and aperiodic gratings for use as couplers in opticalwaveguides. Efficiencies close to the theoretical maximums areobtainable with this method.

The structures achieved by this method have a narrow bandwidth ofoperation and therefore are suitable to the design of filters.

It is known that whenever an obstruction is placed in the path of anelectromagnetic wave, the energy is scattered into various modes. Suchan obstruction can be created in a waveguide by varying its dimensionsor by changing the material of the dielectric inside it. The method ofthe present invention is directed at finding an optimum scatteringsurface that will scatter essentially all of the energy in the inputmode(s) into one mode or a set of modes desired at the output. Thefollowing steps are used to design such a surface:

1. Specify the application of the device (i.e., the frequency ofoperation, type of device, structure, and size of the input and outputwaveguides, the mode composition of the incident electromagnetic fieldand the required mode composition of the output electromagnetic field);

2. Pick a method of variation (i.e., variation of waveguide shape only,variation of only the material properties of the obstruction orvariation of both the shape and the material);

3. Choose the material to be used for the obstruction;

4. Decide the directions in which the obstruction and/or waveguide shapeand material must vary;

5. Pick a suitable basis function to represent the waveguide shapeand/or material properties in each of the waveguide dimensions;

6. Choose an initial structure approximation (i.e., give some arbitrary(but realistic) values to all the variables (coefficients) in the seriesrepresentations and pick a length, L, for the structure);

7. Formulate the forward solution;

8. Perform a global optimization to find values of the coefficients thatmaximize the output power in the desired output mode(s);

9. (Optional) Obtain multiple designs (i.e., repeat steps 5 through 8 tocome up with a number of designs and select an optimal design under thecircumstances); and

10. Fabricate the device.

OBJECTS AND ADVANTAGES OF THE INVENTION

Accordingly, it is an object and advantage of the present invention toprovide a method for designing compact, efficient waveguide mode controland conversion devices useable in microwave and optical applications.

It is a further object and advantage of the present invention to providea method for designing mode converters, mode filters, waveguideadapters, mode launchers, power splitters, phase shifters and aperiodicgratings for use as couplers in waveguides.

It is a further object and advantage of the present invention to providea methodology for creating aperiodic mode control and mode conversionsurfaces which are more compact than conventional periodic structuresused for these purposes.

Yet another object and advantage of the present invention is to providea method for the design of narrowband filters, specifically for opticalapplications.

These and many other objects and advantages of the present inventionwill become apparent to those of ordinary skill in the art from aconsideration of the drawings and ensuing description of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a conventional periodic grating used inmode control and conversion in accordance with the prior art.

FIG. 2 is a schematic diagram of an input waveguide section, a modeconversion/control element and an output waveguide section in accordancewith a presently preferred embodiment of the present invention.

FIG. 3 is a schematic diagram of an input waveguide section, a modeconversion/control element and an output waveguide section in accordancewith a presently preferred embodiment of the present invention.

FIG. 4 is a schematic diagram of a mode conversion/control elementdisposed within a waveguide section in accordance with a presentlypreferred embodiment of the present invention.

FIG. 5 is a schematic diagram of a mode conversion/control elementformed of slabs of materials of varying indices of refraction disposedin an optical structure in accordance with a presently preferredembodiment of the present invention.

FIG. 5A is a schematic diagram of a mode conversion/control elementformed of slabs of materials of varying indices of refraction.

FIG. 6 is a diagram showing the construction of a mode converter inaccordance with a presently preferred embodiment of the presentinvention.

FIG. 7 is an exploded diagram showing the construction of a modeconverter in accordance with a presently preferred embodiment of thepresent invention.

FIG. 8 is a diagram showing an assembled version of the mode converterin accordance with FIG. 7.

FIGS. 9 and 10 depict an SMA wave launcher in accordance with apresently preferred embodiment of the present invention.

FIG. 11 is a diagram illustrating a simplified scattering structurewithin a parallel plate waveguide in accordance with a presentlypreferred embodiment of the present invention.

FIG. 12 is a diagram illustrating an optimization surface for TE₁ to TE₂conversion in accordance with the scatterer of FIG. 11.

FIG. 13 is a diagram illustrating an optimization surface for TE₁ to TE₆conversion in accordance with the scatterer of FIG. 11.

FIG. 14 is a diagram showing the construction of a TE₁ to TE₂ converterin a parallel plate waveguide in accordance with a presently preferredembodiment of the present invention.

FIG. 15 is a series of four diagrams showing the sequence ofoptimization of the structure for a TE₁ to TE₂ mode converter structurein a parallel plate waveguide in accordance with a presently preferredembodiment of the present invention.

FIG. 16 is a diagram comparing three distinct designs for a TE₁ to TE₂mode converter structure in a parallel plate waveguide in accordancewith a presently preferred embodiment of the present invention.

FIG. 17 is a chart comparing performance parameters of the threedistinct designs shown in FIG. 16.

FIG. 18 is a diagram showing the structure of a TE₁ to TE₂ modeconverter structure in a parallel plate waveguide in accordance with apresently preferred embodiment of the present invention.

FIG. 19 is a diagram showing the structure of a TE₀₂ to TE₀₁ modeconverter structure for circular waveguide in accordance with apresently preferred embodiment of the present invention.

FIG. 20 is a plot of efficiency versus frequency for the TE₀₂ to TE₀₁mode converter structure of FIG. 19.

FIG. 21A is a plot of width profile versus distance along the zdirection for a prior art circular waveguide TE₀₂ to TE₀₁ mode converterin accordance with M. J. Buckley, et al., "A Single Period TE₀₂ to TE₀₁mode converter in a highly overmoded circular waveguide," I.E.E.E.Transactions on Microwave Theory and Techniques, Vol. 39, No. 8 (August,1991), pp. 1301-1306.

FIG. 21B is a plot of efficiency versus frequency (GHz) for a prior artcircular waveguide TE₀₂ to TE₀₁ mode converter in accordance with M. J.Buckley, et al., "A Single Period TE₀₂ to TE₀₁ mode converter in ahighly overmoded circular waveguide," I.E.E.E. Transactions on MicrowaveTheory and Techniques, Vol. 39, No. 8 (August, 1991), pp. 1301-1306.

FIG. 22 is a chart comparing the length and conversion efficiency of the"Previous" design of FIGS. 21A and 21B with the "Present" design ofFIGS. 19 and 20.

FIG. 23 is a diagram of a grating design for a circular waveguide TE₀₆to TE₀₁ mode converter for operation at 140 GHz in accordance with apresently preferred embodiment of the present invention.

FIG. 24 is a plot of efficiency versus frequency (GHz) for a prior artcircular waveguide TE₀₆ to TE₀₁ mode converter for operation at 140 GHzin accordance with K. Kumric et al., "Optimization of Mode Convertersfor Generating the Fundamental TE₀₁ Mode from TE₀₆ Gyrotron Output at140 GHz," International Journal of Electronics, Vol. 64, No. 1 (January,1988), pp. 77-94.

FIG. 25 is a chart comparing the length and conversion efficiency of the"Previous" design of FIG. 24 with the "Present" design of FIG. 23.

FIG. 26 is a pair of diagrams comparing a pair of designs for a circularwaveguide TE₁₁ to TM₁₁ mode converter structure each designed inaccordance with a presently preferred embodiment of the presentinvention.

FIG. 27 is a chart comparing the length and conversion efficiency andother performance parameters of the "Design 1" design of FIG. 26 withthe "Design 2" design of FIG. 26.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Those of ordinary skill in the art will realize that the followingdescription of the present invention is illustrative only and is notintended to be in any way limiting. Other embodiments of the inventionwill readily suggest themselves to such skilled persons from anexamination of the within disclosure.

The present invention is directed to a new method for the design andfabrication of mode control devices which can result in aperiodic,totally rough structures. These devices can be developed for free spacewave propagation or for microwave and optical waveguides. Previously itwas believed that there are only certain type of shapes (mostly periodicstructures) that can be used to develop mode control devices. Inaccordance with the method set forth below, however, the domain of allpossible shapes and materials is explored for a scattering obstruction,which when placed in the path of the incoming electromagnetic wave willconvert power from a set of modes in the incoming electromagnetic wave(one or more) to any of a set of modes at the output. The method taughthere is completely general and does not restrict itself to a specifictype of pattern variation. Structures obtained with this method haveaperiodic variations and can be very irregular in shape. Thesestructures are generally very short as compared to their periodiccounter-parts obtained using coupled mode theory.

OVERVIEW

The basic concept is to place an obstruction in the path of the incomingelectromagnetic field. The shape, size, and material of the obstructionis totally arbitrary. When the incoming field interacts with theobstruction, it scatters into various modes of propagation. A procedureis then adopted to optimize the shape, size, and material of theobstruction so as to maximize the power scattered into the required modeat the output, so that close to 100% of the input power is transformedinto the desired mode or that the output mode(s) has the desiredcharacteristic. The size and shape of the input and output waveguides isarbitrary. Also the obstruction can protrude outside the dimension ofthe waveguide and the waveguide wall dimensions can vary in the modeconverter section.

METHODOLOGY

The variation in the shape of the waveguide and/or material of theobstruction, in each of the three dimensions (the three dimensions forrectangular and parallel plate waveguides are the Cartesian coordinates:x, y and z; for circular waveguides, these are the cylindricalcoordinates: r, φ and z), can be represented by suitably weighting a setof basis functions, e.g., delta functions, step functions, trigonometricfunctions, Bessel functions and other functions as would be readilyunderstood by those of ordinary skill in the art.

To illustrate the idea consider an obstruction placed in a circularwaveguide. In the most general case, both the shape of the waveguide andmaterial properties of the obstruction will be changed in all directionsas shown in FIG. 3. However, to keep it simple assume that the shape andmaterial properties of the obstruction do not vary in the radial, r, andcircular, φ, dimensions as in FIG. 2. This means that the obstruction 16fills the whole waveguide 18 and its dimension and material propertiesvary only as a function of z (the distance along the waveguide in thedirection travelled by the incoming electromagnetic wavefront). Such astructure would be able to convert only the radial suffix of theincoming mode. Specifically, the following conversions are possible:

TE_(mn) to TE_(mp)

TE_(mn) to TM_(mp)

TM_(mn) to TE_(mp)

TM_(mn) to TM_(mp)

Before the design procedure starts it is necessary to specify thecomposition of the input electromagnetic field and the outputelectromagnetic field. It is also necessary to specify some parametersof the output magnetic field which are to be optimized to obtain therequired output. In the present case, the input is a combination ofTE_(mn) modes while output is a TE_(mp) mode. The optimization parameteris thus the power in mode TE_(mp).

The z-variations in the shape and electrical/magnetic materialproperties of the obstruction can be represented by using some suitablebasis functions. Some examples are given below:

USING THE WAVEGUIDE SHAPE

Δr(z)=r₀ δ(z)+r₁ δ(z-z₁)+r₂ δ(z-z₂)+ . . . (δ is the Kronecker deltafunction)

OR

Δr(z)=r₀ U(z)+r₁ U(z-z₁)+r₂ U(z-z₂)+ . . . (U is the step function)

OR

Δr(z)=r₀ sin (z)+r₁ sin (3z)+r₂ sin (5z)+ . . .

OR

Δr(z)=r₀ J₀ (z)+r₁ J₁ (z)+r₂ J₂ (z)+ . . . (J_(N) are the Besselfunctions)

where 0<z<L; L is the maximum length of the obstruction.

If r is the radius of the input waveguide then Δr(z) is the delta changein waveguide radius as a function of z.

Lower Limit on Δr(z): Δr(z)>-r

Upper Limit on Δr(z): Practical constraint on the largest radialdimension for the waveguide.

USING THE ELECTRICAL PROPERTIES OF THE OBSTRUCTION (DIELECTRIC CONSTANT,ε)

Δε(z)=e₀ δ(z)+e₁ δ(z-t₁)+e₂ δ(z-t₂)+ . . . (δ is the Kronecker deltafunction)

OR

Δε(z)=e₀ U(z)+e₁ U(z-t₁)+e₂ U(z-t₂)+ . . . (U is the step function)

OR

Δε(z)=e₀ sin (z)+e₁ sin (3z)+e₂ sin (5z)+ . . .

OR

Δε(z)=e₀ J₀ (z)+e₁ J₁ (z)+e₂ J₂ (z)+ . . . (J_(N) are the Besselfunctions)

where 0<z<L; L is the maximum length of the obstruction.

If ε is the dielectric constant of the material in the input waveguidethen Δε(z) is the delta change in ε as a function of z.

USING THE MAGNETIC PROPERTIES OF THE OBSTRUCTION (MAGNETIC PERMEABILITY,μ)

Δμ(z)=u₀ δ(z)+u₁ δ(z-d₁)+u₂ δ(z-d₂)+ . . . (δ is the Kronecker deltafunction)

OR

Δμ(z)=u₀ U(z)+u₁ U(z-d₁)+u₂ U(z-d₂)+ . . . (U is the step function)

OR

Δμ(z)=u₀ sin (z)+u₁ sin (3z)+u₂ sin (5z)+ . . .

OR

Δμ(z)=u₀ J₀ (z)+u₁ J₁ (z)+u₂ J₂ (z)+ . . . (J_(N) are the Besselfunctions)

where 0<z<L; L is the maximum length of the obstruction.

If μ is the magnetic permeability of the material in the input waveguidethen Δμ(z) is the delta change in μ as a function of z.

Note that for delta functions if the difference between two consecutivez_(n) 's is negligibly small and the difference between two consecutiveΔr(z) values is much less than a wavelength, then the aboverepresentation can be used to model continuous surfaces, which is themost general case. For step functions the same can be done byrestricting the difference between two consecutive Δr(z) and twoconsecutive z_(n) 's to be much less than a wavelength. The other twofunctions mentioned above automatically result in continuous surfaces.

If one type of function is used for the waveguide shape, it is notnecessary that the same type of function be used for materialproperties. The functional representation of Δr(z), Δε(z), and Δμ(z) canbe totally different.

The variables r₀, r₁, r₂, . . . ; e₀, e₁, e₂, e₃, . . . ; u₀, u₁, u₂,u₃, . . . ; z₁, z₂, z₃, . . . , t₁, t₂, t₃, . . . , d₁, d₂, d₃, . . .for step, delta, sine, Bessel or other functions; and length L uniquelyrepresent the shape and material of the obstruction. The power scatteredby this structure in a particular mode, P₀, at the output of thestructure is then a function of all these variables, i.e.,

P₀ =P₀ (r₀, r₁, r₂, . . . ; e₀, e₁, e₂, e₃, . . . ; u₀, u₁, u₂, u₃, . .. ; z₁, z₂, z₃, . . . , etc., L)

In accordance with the design methodology of the present invention, oneoptimizes the power P₀ as a function of these variables so that nearly100% of the input power is, for example, converted to the required mode.Optimized values of the variables then represent the required design ofthe mode control device.

It may be noted here that there is a potentially infinite number ofvariables involved in representing the obstruction in the most generalcase. To make the solution practically viable it is preferable totruncate each infinite series of basis functions to a finite number ofterms. Thus, one can express P₀ as:

P₀ (r₀, r₁, r₂, . . . , r_(n), e₀, e₁, e₂, e₃, . . . , e_(m), u₀, u₁,u₂, u₃, . . . , u_(q), L)

where the series for Δr(z) is truncated to n+1 terms, for Δε(z) it ism+1 terms, and Δμ(z) is q+1 terms.

Even after truncation, the number of variables for optimization may bevery large. To optimize say 50 variables simultaneously is often a verydifficult problem. Most global optimization techniques work best whenthe number of variables is limited to between two and five variables. Inorder to optimize the mode converter a hierarchical, sectionaloptimization procedure has been developed.

HIERARCHICAL OPTIMIZATION

In this procedure one starts with a very coarse estimate for thefeatures of the mode converter. This is done by just a few terms in thebasis function representation of shape/material and a small length L.This way the initial number of variables is small. These variables arethen optimized in order to obtain a coarse estimate of the finalstructure. Next, more terms are added to the series and L is alsoincreased, thus increasing the number of variables and also refining therepresentation of the mode transducing obstruction. Optimization isagain carried out and the procedure is repeated until a suitable modeconverter is identified. Because of a small number of variables inearlier stages a lot of computation time is saved.

SECTIONAL OPTIMIZATION

As one moves up in the hierarchical optimization procedure the task ofoptimization becomes even more difficult due to the increase in thenumber of variables. In order to perform a global optimization of all ofthese variables a sectional optimization procedure is preferablyemployed. For example, assume that one is using a global optimizationtechnique which converges best when the number of variables isrestricted to two, but the number of variables to be optimized is 50.The variables may then be optimized two at a time, starting with thefirst two. While optimizing a set of two the rest of the variables arekept constant. When all the 50 variables have been optimized once, goback to the first set and repeat the sequence. The sectionaloptimization sequence is continued until a global solution is achievedfor all the 50 variables.

It may be observed that as one truncates the series to a small number ofterms, at the start of hierarchical optimization, one restricts thedomain of the structures that can be formulated for mode conversion.During optimization one searches in this restricted domain ofstructures. If a desired solution is obtained, the process is halted andthe solution is accepted, otherwise the number of terms in the series isincreased and/or the length, L, is increased and a search is carried outin a larger domain of possible structures. This procedure is continueduntil an appropriate structure is identified. Thus no presumption ismade about the final shape of the mode converter.

The hierarchical procedure defined above does not result in uniquesolutions for mode conversion structures because the number of freevariables is much greater than the cost function constraints. Dependingupon the initial guess for optimization, type of basis functions, andnumber of terms in the series various solutions can be obtained for thesame problem. Out of the various solutions found through the designprocess only those structures may be considered that are feasible tofabricate using the available fabrication procedures. Normally a numberof solutions would be obtained. Each would be assessed for itsfeasibility of construction and the easiest to fabricate would be chosenfor development.

DESIGN OF MODE CONTROL DEVICES USING ARBITRARY STRUCTURE OPTIMIZATION

1. SPECIFY THE APPLICATION OF THE DEVICE

At this point one must determine and specify the basic known parametersof the device to be designed. This requires the following to bedetermined:

(a) Frequency of operation, type, structure, and size of the input andoutput waveguides. (Microwave and lower/upper frequencies: free space,parallel plate, rectangular, circular, elliptical, etc. waveguides, andtransmission lines like microstrip, stripline, coaxial etc. Optical andlower/upper frequencies: free space, slab, fiber etc. waveguides);

(b) Mode composition of the incident electromagnetic field;

(c) Required mode composition and characteristics of the outputelectromagnetic field; and

(d) Parameters of the output electromagnetic field which uniquelyspecify the field and are to be optimized.

2. PICK A METHOD OF VARIATION

Pick any of the following methods for generating a wave obstructingstructure:

(a) Variation of waveguide shape only;

(b) Variation of only the material properties of the obstruction; and

(c) Variation of both the shape and the material.

Which of the above three methods one chooses depends upon thesuitability of fabrication for a particular application and waveguidetype. Methods 2a, 2b and 2c may be used for both microwave waveguidesand optical waveguides. For free space application there can be twocases: reflection and transmission. In the reflection case theobstruction would be a rough aperiodic reflecting surface; in thetransmission case a dielectric obstruction with varying shape andproperties can be used.

3. CHOOSE THE MATERIAL

Choose the material to be used for the obstruction. If method 2a is usedthen the material would preferably be the same as that used for theinput waveguide.

4. DECIDE THE DIRECTIONS OF PERTURBATION

Depending upon the input mode structure and the required output mode,decide the directions in which the obstruction and/or waveguide shapeand material must vary. For example for a TE_(mn) mode, in a rectangularwaveguide, the following conversions can be achieved:

TE_(mn) to TE_(mp) by varying the structure in y dimension.

TE_(mn) to TE_(pn) by varying the structure in x dimension.

where the "m" subscript refers to the x-direction and the "n" subscriptrefers to the y-direction.

5. PICK A SUITABLE BASIS FUNCTION

Pick a basis function to represent the waveguide shape and/or materialproperties in each of the waveguide dimensions. Again, the selection ofthe basis functions would depend upon the particular application andfabrication procedure, e.g., sinusoidal basis functions may be moresuitable when the mode converter is going to be pre-formed or molded. Byselecting step functions for a circular microwave waveguide, a very easyfabrication technique may be implemented as shown below. Truncate theinfinite series representation to a finite number of terms.

6. CHOOSE AN INITIAL STRUCTURE APPROXIMATION

Give some arbitrary (but realistic) values to all the variables(coefficients) in the series representations. Also pick a length, L, forthe structure. Initially choosing these values defines an initial"guess" for the shape and material of the obstruction. This guess willact as the initial point for the optimization procedure. After someexperience in dealing with a specific application a designer can usehis/her intuitive feeling as to what type of initial guess would resultin faster convergence of optimization and best results. See thediscussion of initial structure approximation, below.

7. FORMULATE THE FORWARD SOLUTION

Given the information in steps 1 through 5, the forward solution to thescattering problem can be formulated. The goal is to find theelectromagnetic field at the exit plane of the obstruction (O-O' inFIG. 1) when a given field is incident on the input plane (I-I' in FIG.1). Any boundary value solution technique can be used to solve for theoutput field. A very useful commercial software package for this purposeis HFSS (High Frequency Structure Simulator) available from theHewlett-Packard Corporation of Cupertino, Calif. Other software packagesare also available to perform functions like this as is well known tothose of ordinary skill in the art. From the solution of theelectromagnetic field, the power coupled into the required outputmode(s), P₀, in the output waveguide can be evaluated. P₀ is a functionof all the defining variables for the obstruction and needs to beoptimized (maximized) to find the required structure.

8. PERFORM A GLOBAL OPTIMIZATION

Select a global optimization technique for constrained optimization. Itis preferable to use constrained optimization because most of the timethere would be realistic constraints on the minimum and maximum valuesof various variables (coefficients). For example, the radius of acircular waveguide can't be less than or equal to zero. Similarly thereare limits to which e can be realistically varied for a dielectric.Routines for constrained optimization are available in standard C andFortran libraries, and also in software packages like MATLAB availablefrom The Mathworks, Inc. of Natick, Mass. Most of these routines workbest when the number of optimization variables is small, say 2. Use thehierarchical, sectional optimization procedure explained in the previoussection to optimize P₀ as a function of the properties of theobstructing structure. As optimization is continued the number ofvariables may be increased to more finely define the obstruction, thusachieving more flexibility in optimization and reaching a desired valueof P₀ as a percentage of the total input power.

If there is more than one parameter that specifies the output field,e.g., powers and phases of more than one mode, then the optimizationbecomes even more difficult. For example, consider the case where theoutput electromagnetic field has two modes with equal power in each.Then we can maximize the following two parameters:

1. P₀, the total additive power in the two modes, i.e., P₀ =P₁ +P₂,where P₁ and P₂ are the powers in the two modes respectively.

2. R=P_(small) /P_(large), where P_(small) is the smaller of the twovalues P₁ and P₂ and P_(large) is the larger of the two values.

Thus when carrying out the design of a specific mode control/conversionelement, the additional items (for example) would need to be specified:

Output Field: 50% TE₁₁ and 50% TM₁₁

Optimize: P₀ =Total output power in TE₁₁ (P₁) and TM₁₁ (P₂) modes.P_(small) is the smaller of the two mode powers P₁ and P₂ and P_(large)is the larger of the two mode powers.

Optimize: R=P_(small) /P_(large)

9. OBTAIN MULTIPLE DESIGNS (OPTIONAL)

This step is optional but preferred. Repeat steps 5 through 8 to come upwith a number of different designs based upon different initial startingpoints for the structures (step 6). Select one of these designs to buildthe mode control/conversion device based on simplicity of structure,bandwidth of operation, size, ease of fabrication, and the ability ofthe design to tolerate fabrication errors (maximum possible in thefabrication technique) without drastically affecting the value of P₀.

10. FABRICATE THE DEVICE

Fabricate the mode control device using an appropriate fabricationtechnique.

DESIGN EXAMPLES

What follows are examples which demonstrate the techniques used todesign different types of mode control/conversion devices (in differentwaveguide geometries) using the methods of the present invention. Thefollowing descriptions are based upon the same basic steps described inthe previous section.

Example 1 TE_(mn) to TE_(pq) Mode Converter in a Rectangular WaveguideUsing Only Material Variation

1. Specify the application of the device:

(a) Frequency: 4 GHz

Input Waveguide: Dielectric filled (ε) metallic wall rectangularwaveguide with dimensions "a" in the x-direction and "b" in they-direction.

Output Waveguide: Same waveguide as at the input.

(b) Input EM Field: A known combination of TE_(mn) modes.

(c) Output EM Field: Only TE_(pq) mode.

(d) Output Parameter: Power in TE_(pq) mode.

2. Pick a method of variation:

Here it is desired to develop the mode converter by putting a dielectricmaterial inside the waveguide 20 at box 22 as shown in FIG. 4. Thus, themethod of variation in the material properties of the obstruction isselected and the waveguide dimensions remain constant. As theobstructing device 22 is a dielectric material, its magneticpermeability, μ, is also assumed to be constant.

3. Choose the material:

Choose a suitable material for the structure. The material should besuch that its e can be varied significantly and various shapes can befabricated easily using this material. A wide variety of such materialsare known to those of ordinary skill in the art. Examples include:teflon and ceramic.

4. Decide the direction of perturbation:

Because it is desired to convert from TE_(mn) modes to a TE_(pq) mode,i.e., both suffixes need to be converted. ε will thus be allowed to varyin all the three dimensions x, y, and z.

5. Pick a suitable basis function:

The variation in E is represented by using sinusoidal basis functionssuch that:

    Δε(x,y,z)=x.sub.0 sin (x)+x.sub.1 sin (3x)+ . . . +y.sub.0 sin (y)+y.sub.1 sin (3y)+ . . . +z.sub.0 sin (z)+z.sub.1 sin (3z)+ . . .

The series is truncated to two terms in each dimension, yielding:

    Δε(x,y,z)=x.sub.0 sin (x)+x.sub.1 sin (3x)+y.sub.0 sin (y)+y.sub.1 sin (3y)+z.sub.0 sin (z)+z.sub.1 sin (3z)

6. Choose an initial structure approximation:

Assign suitable values to x₀, x₁, y₀, y₁, z₀, z₁ and also chose lengthsL₁, L₂, and L₃.

7. Formulate the forward solution:

The forward solution is developed by writing a FEM (Finite Element Code)or by using HFSS software to find power P₀ in the mode TE_(pq). Then P₀=P₀ (x₀, x₁, y₀, y₁, z₀, z₁, L₁, L₂, L₃)

8. Perform a global optimization:

BCPOL, an IMSL (International Mathematical and Statistical Library)constrained optimization routine is preferably used for optimizing P₀.Variables x₀, x₁, y₀, y₁, z₀, z₁, L₁, L₂ and L₃ are optimized using thehierarchical, sectional optimization procedure explained in the previoussection. The optimized variables then define the structure of thedielectric obstruction for mode conversion. BCPOL is available from IMSLof 2500 City West Blvd., Houston, Tex.

9. Obtain multiple designs (optional):

Optionally repeat steps 5 through 8 to generate a variety of designsbased upon different sets of initial values for the variables: x₀, x₁,y₀, y₁, z₀, z₁, L₁, L₂ and L₃. Select the best design based onperformance and ease of fabrication.

10. Fabrication:

Fabricate the final design using an appropriate technique.

Example 2 Free Space Optical Wavelength Filter: Bragg Reflector

This example provides a methodology for preparing modecontrol/conversion devices for use in optical waveguide systems, e.g.,optical fiber. In order to be able to more fully utilize the availableoptical fiber spectrum for communication of data, wavelength divisionmultiplexing of the signal can be used. The limitation of the systembecomes how close the lines can be spaced. The LASER line needs to be ofvery narrow bandwidth and stable in order for close spacing. Inaddition, narrow spectral linewidth (and hence long coherence length)light is important for metrology.

Conventional periodic Bragg reflectors cannot produce as narrow apassband as aperiodic structures of the same total thickness. Ratherthan relying on end mirrors, the spectral and mode control structurecould be distributed throughout a LASER diode cavity. Using lithographyor special semiconductor material growth procedures known to those ofordinary skill in the art, it is possible to have materials withdifferent refractive index properties distributed throughout the LASERcavity. By controlling the size and location of these materials, it ispossible to also control the optical signal properties of the cavity ina superior fashion to the standard cavity approach. The location andsize of the "inhomogeneities" that are distributed throughout the cavitywould be optimized to achieve the desired result.

In a wavelength division multiplexing system, filters for multiplewavelengths are needed where several wavelengths are passed and theremainder of the spectrum is rejected. Standard filter theory can beused to design a bandpass filter for a single wavelength. If there are,for example, three wavelengths, then superimposing or cascading designsfor each wavelength will not work very well because a filter for onewavelength will not pass the other two effectively. By usingoptimization techniques with aperiodic structures, better filters forthe three wavelengths can be designed. These filters are implemented bychanging the dielectric properties or profile of an optical waveguide(e.g., planar or optical fiber).

Here, the goal is to design a narrow band filter for optical wavelengthsto be used in narrow band distributer Bragg reflector ("DBR") ordistributed feedback ("DFB") LASERs. Currently periodic dielectricvariations, i.e., gratings or Bragg reflectors, are used in DBR LASERsto make them narrow band. In accordance with the technique of thepresent invention, these are replaced with irregular structures theshapes of which are not pre-defined. These structures generally achievenarrower bandwidth of operation than can be achieved by Braggreflectors. Thus in this way the present invention can be used to designnarrow wavelength filters for optical applications.

1. Specify the application of the device:

(a) Frequency: Optical LASER Frequency (Wavelength=1480 nm)

(b) Input EM Field: Normally incident single plane wave in free space(say output of a LASER).

(c) Output EM Field: Normally exiting single plane wave in free space.

(d) Output Parameter: Power in the output wave.

2. Pick a method of variation:

For obvious reasons choose method 2b: Variation of material propertiesof the obstruction.

3. Choose the material:

The scattering structure will consist of a thick dielectric slab 24schematically shown in FIG. 5 whose dielectric constant varies in the zdirection only (the direction of the incoming wave). It is preferable touse a material that is easy to use and can have maximum variation of e.Al_(x) Ga_(1-x) As is suited for such an application. Other suitablematerials will also be readily apparent to those of ordinary skill inthe art. By changing "x" in the chemical formula, a large variation in εcan be achieved (8.8 to 12.8). Using an MBE (Molecular Beam Epitaxy)machine it is possible to grow layers of Al_(x) Ga_(1-x) As with varyingthicknesses. A structure as shown in FIG. 5 made up of slabs of Al_(x)Ga_(1-x) As which have essentially infinite transverse dimensions incomparison to the spot radius of the input LASER beam is used toimplement the filter.

4. Decide the direction of perturbation:

The dielectric variation will only be in the z direction.

5. Pick a suitable basis function:

For the type of structure proposed in step 3, an ideally suited basisfunction is the step function. Thus:

Δε(z)=e₀ U(z)+e₁ U(z-t₁)+e₂ U(z-t₂)+ . . . (U is the step function)

where each of the variables e₀, e₁, e₂, e₃, . . . can vary from 7.8 to11.8 and Δε is the difference between the ε of the material and the ε offree space. The only limits on t₁, t₂, t₃, . . . are as follows:

t_(i+1) -t_(i) ≧t_(min) for all i

t_(i+1) -t_(i) ≦t_(max) for all i

t_(min) : Minimum sheet thickness that can be generated by the MBEprocess. It is equal to approximately one atomic layer.

t_(max) : Practically feasible maximum thickness of a slab. It isgenerally equal to a wavelength at the operating frequency of the LASER.

Truncating the series to a finite solution:

P₀ =P₀ (e₀, e₁, e₂, . . . , e_(m), t₁, t₂, . . . , t_(n), L)

6. Choose as initial structure approximation:

As an initial "guess" one may alternately pick values of e_(i) 's to be7.8 and 11.8, select t_(i+1) -t_(i) =0.5 wavelength for all i's, andpick an initial length, L, of 5 wavelengths.

The dielectric constants (10 in number) and widths of the slabs (10 innumber) are then the finite number of variables which uniquely identifythe obstructing structure 24.

7. Formulate the forward solution:

The forward problem is easy to solve. There is a standard analyticexpression available to solve for the transmitted power through a seriesof dielectric slabs.

The transmitted power for a stack of three dielectrics is calculated asfollows. See FIG. 5A. Let η₁, η₂, η₃ be the characteristic impedances inthe three mediums 25a, 25b and 25c. Then the impedance seen at the inputto medium 25b is given as:

    Z.sub.L =η.sub.2 ((η.sub.3 cos k.sub.2 l+jη.sub.2 sin k.sub.2 l)/(η.sub.2 cos k.sub.2 l+jη.sub.3 sin k.sub.2 l))

where k₂ is the wave number in medium 25b. Then the reflectioncoefficient is given as:

    ρ=((Z.sub.L -η.sub.1)/(Z.sub.L +η.sub.1))

    P.sub.transmitted =P.sub.incident (1-|ρ|.sup.2).

The output power, P₀, at wavelength 1480 nm is then a function of P₀(e₀, e₁, e₂, . . . , e_(m), t₁, t₂, . . . , t_(n), L).

8. Perform a global optimization:

The FORTRAN IMSL routine BCPOL is preferably used to globally optimizeP₀. For this simple problem BCPOL could easily optimize up to 8variables simultaneously. The constrained optimization limits given instep 5 for various variables are given as input to the BCPOL program.The sectional, hierarchical optimization technique is then used todetermine the optimized structure. As optimization progresses, thenumber of optimization variables is increased for more flexibility byadding more slabs at the beginning or end of the structure, thusincreasing L. The process is stopped when almost 100% power istransmitted through the structure at the nominal wavelength.

9. Obtain multiple designs (optional):

Using different initial guesses and design decisions (as in step 6) avariety of structures are designed. The 3 dB bandwidth for eachstructure is obtained by solving the forward electromagnetic problem asa function of frequency, i.e., by evaluating the transmitted power atvarious frequencies and plotting power versus frequency to determine the3 dB points. The device with the least bandwidth is chosen forfabrication.

10. Fabricate the device:

The dielectric slab structure is fabricated by growing layers of Al_(x)Ga_(1-x) As by MBE (Molecular Beam Epitaxy) or any other suitabletechnique.

Example 3 Circular Waveguide TE₁₁ to TM₁₁ Microwave Mode Converter fromSmaller to a Larger Waveguide

This structure can be called a mode converter, a mode launcher, or awaveguide transition. It is a mode converter because it converts a TE₁₁mode to a TM₁₁ mode. It is a mode launcher because it demonstrates thatany type of mode can be launched into an overmoded large waveguide whichis fed by a small waveguide having a single known mode in it.

1. Specify the application of the device:

(a) Frequency: 9.94 GHz (λ=3 cm).

Input Waveguide: Air-filled metallic wall circular waveguide with radius0.3895".

Output Waveguide: Air-filled metallic wall circular waveguide withradius 0.812".

(b) Input EM Field: Only composed of TE₁₁ mode.

(c) Output EM Field: Only composed of TM₁₁ mode.

(d) Output Parameter: Power in TM₁₁ mode.

2. Pick a method of variation:

Method 2a is selected (variation of waveguide shape) because this iseasy to demonstrate and also results in a new way of fabricatingmicrowave waveguide mode converters, as will be discussed later.

3. Choose the Material:

To keep it simple, choose an air-filled mode converter section.

4. Decide the direction of perturbation:

Because both TE₁₁ and TM₁₁ modes are circularly symmetric, a change inthe radial dimension of the waveguide as a function of z would besuitable for such a conversion.

5. Pick a suitable basis function:

In order to demonstrate a very inexpensive and modular fabricationtechnique for microwave mode converters select step functions torepresent the delta variation in radius as a function of z. Then:

Δr(z)=r₀ U(z)+r₁ U(z-z₁)+r₂ U(z-z₂)+ . . . (U is the step function)

The following restrictions are used on the range of possible values forr₀, r₁, r₂, . . . and z_(i) 's:

r_(i) 's should be selected so that the radius of the mode convertersection at no place is zero or less and is not greater than r_(max)(1.75").

z_(i+1) -z_(i) =Δs where the value of Δs, the step size, will be avariable in the optimization procedure, i.e., the power P₀ in the TM₁₁mode will depend upon the following values:

P₀ =P₀ (r₀, r₁, r₂, . . . , r_(n), Δs, L)

where the series has been truncated to n+1 values.

Note that in this formulation positive values of r_(i) 's are permitted,i.e., the structure can protrude outside the walls of the waveguide(see, e.g., FIG. 3). It has been found through experimentation thatprotrusions outside the waveguide results in quicker convergence of theoptimization solution and also results in shorter mode converters. Whatshould be the size of the largest protrusion is a design decision. Asthe largest protrusion radius, r_(max), is increased, the computationtime for the forward solution increases exponentially. In some cases thecomputation time could be prohibitive to achieve optimizationconvergence. Also it is desirable to limit the radial size of the modeconverter to keep the structure compact.

6. Choose an initial structure approximation:

Initially only four terms from the series of step functions are includedand use the following values:

r₁ =0.2355", r₂ =0.25", r₃ =0.375", r₄ =-0.25", Δs=0.2505" and L=1.002"

It is desired to fabricate sections of this mode converter out ofcommonly available 0.2505" thick aluminum sheet. Therefore, the Δs areheld constant and are not included as a variable in the optimizationprocedure. This is not required as the Δs could be varied as well, ifdesired.

7. Formulate the forward solution:

The mode converter structure defined above consists of equally spacedwaveguide discontinuities. Given the information in steps 1 through 6the power in the modes generated by the structure can be calculatedusing a variety of methods. Two of these methods are Finite ElementMethod (FEM) and the Mode Matching Method. Hewlett Packard's commercialsoftware HFSS also has the capability to solve for waveguidediscontinuities. The power P₀ can therefore be written as a function ofthe various variables, i.e.,

P₀ =P₀ (r₀, r₁, r₂, r₃, L)

8. Perform a global optimization:

BCPOL is again preferably used for constrained optimization of thevariables. Constraints as given in step 5 are used as inputs to theBCPOL algorithm. It was found that the BCPOL solution, in this case,converged faster if the number of variables were restricted to 2. Thus,sectional optimization was employed. To reduce the total time in thecalculation of the forward solution, the scattering effect of the wholestructure is also calculated in sections. While two of the variables arebeing optimized, the solution for the other variables is only calculatedonce and stored in memory. This technique saves a great deal of time,especially when there are a large number of variables.

In the hierarchical optimization procedure, the number of variables canbe increased in two ways; by reducing the value of Δs, or by increasingthe overall length of the structure. The technique of reduction in Δscan be used until Δs_(min) is reached, which is the minimum acceptablethickness of each disc in the structure. Δs_(min) is chosen as afabrication parameter. In this case Δs=Δs_(min) =0.2505". Thus, the onlyoption that there is to vary is to increase L (i.e., the number ofdiscs). The value of L is increased gradually during the hierarchicalprocedure, which increases the domain of possible structures. Theprocedure is stopped when power in the TM₁₁ mode is close to 100%.

9. Obtain multiple designs (optional):

Using different initial guesses and design decisions (as in step 6; whenand where to add more steps etc.) various mode converters were designed.The bandwidth of operation was calculated for each design and alsoestimates were generated as to how much the operation of each wasaffected by incorporating realistic fabrication errors. Based on thesefactors the best design was selected for construction. The total lengthof the finally designed mode converter is 2.505"=10*0.2505" and itsconversion efficiency is 99.5%. A cross-sectional view of the TE₁₁ toTM₁₁ circular waveguide mode converter is shown in FIG. 6.

10. Fabricate the device:

The waveguide mode converter may preferably be fabricated as describedbelow.

For microwave mode converters one of the biggest advantages of thepresent invention is that the designed mode converters are very compactand short in size compared to earlier designs based on periodic wallperturbations (grating structures). There are two design parameters thataffect the overall length of the designed mode converter, Δs_(min) andr_(max). By reducing Δs_(min) and by increasing r_(max) the overalllength of the mode converter can be reduced. There are, however,practical limits on the minimum value of Δs_(min) and the maximum valueof r_(max). The value of Δs_(min) is restricted by the fabricationprocedure, material used, and fabrication errors. Whereas the maximumvalue of r_(max) is restricted by the available computation time andphysical restrictions on the radial size of the structure depending uponits usage.

Instead of using earlier techniques of pre-forming or molding for thefabrication of microwave mode converters, as with the periodicstructures discussed above, a new modular approach to the constructionof waveguide mode converters may preferably be used. In this approachthe structure of the mode converter is discretized along the z dimensionas shown in FIG. 6. Each discretized section is then like a disc whichcan be machined individually. All the discretized sections can then beput together inside a housing to assemble the complete structure. It wasto demonstrate this idea that step functions were used in the designprocedure for the TE₁₁ to TM₁₁ mode converter. Continuous basisfunctions could have also been used in the design (e.g., sinefunctions). In that case the continuous structure of the mode converterwould have to be discretized to implement the modular fabricationmethod. In such a discretization the difference in the radius of twoconsecutive discs and the width of every disc will have to be kept lessthan about one-twentieth of a wavelength. This is required to maintainan accurate representation of the continuous surface by using a verysmall step size compared to a wavelength. This will increase the numberof discs to be machined. To keep the demonstration of the idea simple,discontinuous basis functions have been used which reduce the number ofrequired discs in the structure.

The assembly of the mode converter 26 is shown in an exploded view inFIG. 7. The thickness of each disc 28a, 28b, 28c, 28d, 28e, 28f, 28g,28h, 28i, 28j in the preferred mode converter of FIG. 6 is 0.2505" andthere are a total of 10 discs. An aluminum sheet with thickness slightlygreater than 0.25" is machined on both sides to smooth its surfaces andto have a uniform thickness of 0.2505". A precision grinding machine isused for this purpose. Ten squares with side dimension slightly greaterthan 4.44" are cut out of the aluminum sheet. The square sections arethen machined to make them into circular discs, each of which has aouter diameter of 4.44". This is the ID (inner diameter) of a 4.5" OD(outer diameter) aluminum tube 32 that will house these discs forconcentricity. Appropriate sized holes 30a, 30b, 30c, 30d, 30e, 30f,30g, 30h, 30i, 30j are drilled in the center of each square (the radiiof these holes are the same as the optimized radii of discs in the modeconverter design).

The ten discs are press fit into aluminum tube 32. The length ofaluminum tube 32 is about 1.5" larger than the total length of the modeconverter 26 (2.505"). This space is to slide in the input and outputwaveguide support units 34, 36, respectively. These support units aremachined out of thick aluminum pieces. The input unit 34 has a centerhole 38 large enough for the input waveguide 40 while the output unit 36has a hole 42 to slide in the output waveguide 44. The input and outputadapters have vertical set screws 46, 48 to hold the two waveguides 40,44 in place. The input and output waveguides 40, 44 are preferablypieces of commercially available copper and brass tubing with average OD0.875" and 1.75", respectively, and with wall thicknesses of 0.032" and0.063", respectively. The whole structure of the mode converter isassembled together by a set of four through holes, nuts and bolts asshown in FIG. 7. The fully assembled mode converter 26 is shown in FIG.8.

The radii of the input and output waveguides 40, 44, respectively, are0.3895" and 0.8120". The radii of the holes in discs 28a-28j for thisparticular application are, respectively, 0.3543", 1.2874", 1.5630",1.5748", 0.8268", 0.9055", 0.8268", 0.9055", 0.9449" and 0.7756".

All components used in this design were commercially available and nospecial machines were used in the procedure. Due to this reason the costof fabrication was very low, unlike more conventional mode converters.

In order to test the performance of the mode converter a TE₁₁ mode wasfirst excited in the input waveguide 40. A microwave source having acoaxial cable output was used for this purpose. An extended center-pinSMA launcher shown in FIGS. 9-10 was mounted on the side wall of theinput waveguide of the mode converter. The radius of the input waveguideis such that at 9.94 GHz it only supports the dominant TE₁₁ mode. TheSMA launcher, due to its impedance mismatch with the waveguide, not onlylaunches the TE₁₁ mode but also a number of higher order evanescentmodes into the waveguide. The length of the input waveguide from the SMAlauncher to the input plane of the mode converter is selected to belarge enough so that any evanescent modes have negligible amplitude atthe mode converter plane. Thus is ensured a pure TE₁₁ mode at the inputof the mode converter. The output of the mode converter was tested usinga far field measurement technique and was found to give a 98.1%conversion efficiency to TM₁₁ mode, which is very close to thecalculated value of 99.5%.

DISCUSSION OF INITIAL STRUCTURE APPROXIMATION

It is logical to ask how arbitrary and wrong can the initial guess beand still have the process work. A solution will be found regardless ofthe initial guess for the iterative optimization solution. How good thesolution is depends on the type of optimization and the closeness of theinitial guess to the final, good solution. With the optimizationsolution in a mode converter application, the goal is to maximize thepower in the desired output mode, thereby minimizing the power in allother reflected and transmitted modes. Another way to view this is thatthe wasted power is being minimized. The optimization surface, which isa function of the variables used (such as waveguide dimension), is veryrough, meaning that there are many local minima, i.e., valleys whoseminima are larger than others (which may be close to the desired zerowasted power and hence global solution). The goal of an optimizationroutine would be to find the global minimum by jumping out of the localvalleys in search of a global solution, meaning the best given theparameter search space. If the optimization algorithm is very good, anyinitial guess can be used. Many approaches are available to accomplishthis task in addition to those described herein.

FIG. 11 shows an example of a simple scattering body 50 within awaveguide 52 of diameter 15 cm at a center frequency of 10 GHz.Scattering body 50 is formed of two 0.5 λ-thick sections, one of heighth₁ and the other of height h₂. The z dimension of each is the same. InFIG. 12 is shown the optimization surface for TE₁ to TE₂ conversion forthe situation depicted in FIG. 11. This is a very simple case. As can beseen easily in FIG. 12, the wasted power is depicted as increasing alongthe vertical axis in the upward direction. The goal of optimization ofP₀, for example, is to obtain a solution with a low value of wastedpower (optimized P₀). Thus the "lower" points on the optimizationsurface which correspond to the indicated step heights for h₁ and h₂ inunits of 0.1 λ are "better" places to be than the local maxima of wastedpower. While a "best" solution may be impossible or difficult to achieveunder many circumstances, many good solutions are available. Thus onereason for pursuing several different starting points is to ensure thatone of the "good" solutions will be obtained, rather than a mere localminimum of the surface.

FIG. 13 depicts an optimization surface for TE₁ to TE₆ mode conversionunder the circumstances of FIG. 11. As can be seen, the surface here ismuch more complex than that of FIG. 12 with many more local minimademonstrating the desirability of starting from a variety of initialpoints to guarantee a "good" solution.

ALTERNATIVE EMBODIMENTS

A number of different solutions to mode conversion and control have beenobtained to date. Several of these are shown in the figures.

FIG. 14 is a diagram showing the construction of a parallel platewaveguide TE₁ to TE₂ converter in accordance with a presently preferredembodiment of the present invention.

FIG. 15 is a series of four diagrams showing the sequence ofoptimization of the structure for a parallel plate waveguide TE₁ to TE₂mode converter structure in accordance with a presently preferredembodiment of the present invention.

FIG. 16 is a diagram comparing three distinct designs for a parallelplate waveguide TE₁ to TE₂ mode converter structure in accordance with apresently preferred embodiment of the present invention.

FIG. 17 is a chart comparing performance parameters of the threedistinct designs shown in FIG. 16.

FIG. 18 is a diagram showing the structure of a parallel plate waveguideTE₁ to TE₂ mode converter structure in accordance with a presentlypreferred embodiment of the present invention.

FIG. 19 is a diagram showing the structure of a circular waveguide TE₀₂to TE₀₁ mode converter structure in accordance with a presentlypreferred embodiment of the present invention.

FIG. 20 is a plot of efficiency versus frequency for the circularwaveguide TE₀₂ to TE₀₁ mode converter structure of FIG. 19.

FIG. 21A is a plot of width profile versus distance along the zdirection for a prior art circular waveguide TE₀₂ to TE₀₁ mode converterin accordance with M. J. Buckley, et al., "A Single Period TE₀₂ to TE₀₁mode converter in a highly overmoded circular waveguide," I.E.E.E.Transactions on Microwave Theory and Techniques, Vol. 39, No. 8 (August,1991), pp. 1301-1306.

FIG. 21B is a plot of efficiency versus frequency (GHz) for a prior artcircular waveguide TE₀₂ to TE₀₁ mode converter in accordance with M. J.Buckley, et al., "A Single Period TE₀₂ to TE₀₁ mode converter in ahighly overmoded circular waveguide," I.E.E.E. Transactions on MicrowaveTheory and Techniques, Vol. 39, No. 8 (August, 1991), pp. 1301-1306.

FIG. 22 is a chart comparing the length and conversion efficiency of the"Previous" design of FIGS. 21A and 21B with the "Present" design ofFIGS. 19 and 20.

FIG. 23 is a diagram of a grating design for a circular waveguide TE₀₆to TE₀₁ mode converter for operation at 140 GHz in accordance with apresently preferred embodiment of the present invention.

FIG. 24 is a plot of efficiency versus frequency (GHz) for a prior artcircular waveguide TE₀₆ to TE₀₁ mode converter for operation at 140 GHzin accordance with K. Kumric et al., "Optimization of Mode Convertersfor Generating the Fundamental TE₀₁ Mode from TE₀₆ Gyrotron Output at140 GHz," International Journal of Electronics, Vol. 64, No. 1 (January,1988), pp. 77-94.

FIG. 25 is a chart comparing the length and conversion efficiency of the"Previous" design of FIG. 24 with the "Present" design of FIG. 23.

FIG. 26 is a pair of diagrams comparing a pair of designs for a circularwaveguide TE₁₁ to TM₁₁ mode converter structure each designed inaccordance with a presently preferred embodiment of the presentinvention.

FIG. 27 is a chart comparing the length and conversion efficiency andother performance parameters of the "Design 1" design of FIG. 26 withthe "Design 2" design of FIG. 26.

Although illustrative presently preferred embodiments and applicationsof this invention are shown and described herein, many variations andmodifications are possible which remain within the concept, scope, andspirit of the invention, and these variations would become clear tothose of skill in the art after perusal of this application. Theinvention, therefore, is not to be limited except in the spirit of theappended claims.

What is claimed is:
 1. A method for creating a design for a waveguidemode control device comprising (the steps of):determining theapplication of the mode control device including its frequency ofoperation, type, structure, size of the input and output waveguides,mode composition of the incident electromagnetic field and the requiredmode composition of the output electromagnetic field; determining amethod of variation of an obstruction to be placed within the modecontrol device; choosing a material composition of said obstruction;determining the directions in which said obstruction may vary;determining a suitable basis function to represent the variations in theobstruction and form an expression utilizing combinations of variablesand said basis function to represent variation of said obstruction in atleast one dimension; selecting an initial structure approximation of theobstruction and thereby selecting actual initial values for saidvariables and a length for the mode control device; formulating asolution for output power in at least one selected output mode as afunction of said variables and said length; performing a globaloptimization to determine a set of values of said variables and lengththat tend to maximize output power in said at least one selected outputmode.
 2. A method according to claim 1, further comprising:repeatedlycarrying out selecting, formulating and performing with different seetsof said initial values to determine different sets of values of saidvariables and length that tend to maximize output power in said at leastone selected output mode.
 3. A method according to claim 2, furthercomprising:fabricating the mode control device in accordance with one ofsaid different sets of values of said variables and length that isnearer a desired solution than others of said different sets of values.4. A method according to claim 1, further comprising:fabricating themode control device in accordance with said set of values of saidvariables and length that tend to maximize output power in said at leastone selected output mode.
 5. A method according to claim 1, wherein:saidbasis function is a Bessel function.
 6. A method according to claim 1,wherein:said basis function is a trigonometric function.
 7. A methodaccording to claim 6, wherein:said trigonometric function is a sinefunction.
 8. A method according to claim 1, wherein:said basis functionis a delta function.
 9. A method according to claim 1, wherein:saidbasis function is the Kronecker delta function.
 10. A method accordingto claim 1, wherein:said basis function is a step function.